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Published December 2007 | Accepted Version
Journal Article Open

Fluctuation Properties of the TASEP with Periodic Initial Configuration

Abstract

We consider the joint distributions of particle positions for the continuous time totally asymmetric simple exclusion process (TASEP). They are expressed as Fredholm determinants with a kernel defining a signed determinantal point process. We then consider certain periodic initial conditions and determine the kernel in the scaling limit. This result has been announced first in a letter by one of us (Sasamoto in J. Phys. A 38:L549–L556, 2005) and here we provide a self-contained derivation. Connections to last passage directed percolation and random matrices are also briefly discussed.

Additional Information

© 2007 Springer Science+Business Media, LLC. Received: 14 December 2006; Accepted: 24 July 2007; Published online: 6 October 2007. P.L. Ferrari would like to thank H. Spohn for useful discussions and for suggesting the compact form of the kernel obtained during our previous work [11]. A. Borodin was partially supported by the NSF grant DMS-0402047 and the CRDF grant RIM1-2622-ST-04. The work of T. Sasamoto is partly supported by the Grant-in-Aid for Young Scientists (B), the Ministry of Education, Culture, Sports, Science and Technology, Japan.

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